Solving inverse problems by Bayesian iterative inversion of a forward model with ground truth incorporation

Inverse problems have been often considered ill-posed, i.e., the statement of the problem does not thoroughly constrain the solution space. In this paper we take advantage of this lack of information by adding informative constraints to the problem solution using Bayesian methodology. Remote sensing problems afford opportunities for inclusion of ground truth information, prior probabilities, noise distributions, and other informative constraints within a Bayesian probabilistic framework. We apply Bayesian methods to a synthetic remote sensing problem, showing that the performance is superior to a previously published method of iterative inversion of neural networks. In addition, we show that the addition of ground truth information, naturally included through Bayesian modeling, provides a significant performance improvement